Praxis Elementary Education: Content Knowledge
Preparing to take the Elementary Education: Content Knowledge?
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Praxis Elementary Education: Content Knowledge Quick Facts
This test is designed for people who are planning to become elementary education teachers. It assesses your knowledge in four main areas: Reading and Language Arts, Math, Social Studies, and Science.
The scoring range for this test is 100 – 200. The passing score depends on different states or agencies. The passing scores for different states and agencies are shown below:
The average score for this test is 169, with an average scoring range of 160 – 179.
This test covers a large number of topics, so it is important to start studying as soon as possible. Once you know your testing date, try to create a schedule that will allow you to cover all of the test topics in a reasonable amount of time. Plan to spend at least several weeks studying so that you are not overwhelmed.
What test takers wish they would’ve known:
- An on-screen scientific calculator will be available for you to use during the test. It is helpful to use the practice calculator on http://www.infinitysw.com/ets so that you feel prepared to use the calculator on the test day.
- Pay close attention to questions that include the word not or except, indicating that you should choose the answer choice that does not apply to that scenario.
- Your score is based on the number of correct answers, so it is better to guess on a question you don’t know than to leave it unanswered.
Information and screenshots obtained from the ETS website: https://www.ets.org/praxis/prepare/materials/5018
Reading and Language Arts
The Reading and Language Arts content category has about 49 questions which make up about 35% of the test.
There are five Reading and Language Arts sections:
- Reading: Foundational Skills
- Reading: Literature and Informational Text
- Speaking and Listening
So, let’s start with Reading: Foundational Skills.
Reading: Foundational Skills
This section tests your knowledge on phonics, phonological awareness, and the role of phonics and fluency in reading development.
Let’s discuss some concepts that will more than likely appear on the test.
Open versus Closed Syllables
An open syllable is a syllable that ends with a vowel. A closed syllable ends in a
consonant. An open syllable will create a long vowel sound, while a closed syllable will have a short vowel sound. Words can have both closed and open syllables in them. For example, in the word “label,” the syllable “la” is open and the syllable “bel” is closed. In the word “paper,” the “pa” is an open syllable and the “per” is a closed syllable.
Onsets and Rimes
An onset is the first sound in a word or syllable, created by a consonant or consonant pair. A rime is the vowel and consonant sounds that come after the onset. For example, in the word “cat,” /c/ is the onset and /at/ is the rime. In the word “shirt,” /sh/ is the onset and /irt/ is the rime.
Students need practice blending onsets and rimes and separating words into onsets and rimes in order to develop their phonemic awareness. As a teacher, you can help students in this area by saying something such as “/cl/ – /ock/” and having students blend it into the word “clock.”
Fluency is the ability to read with accuracy, appropriate speed or pace, and with expression. Fluency is a very important skill for students to develop because it is directly related to reading comprehension. Students who cannot read fluently will have a difficult time understanding what they read. Fluency is something that develops and improves with time, practice, and with modeling from the teacher.
There are three components to reading fluently: accuracy, rate, and prosody.
- Accuracy is being able to read words correctly.
- Rate means reading at an appropriate speed.
- Prosody refers to a student’s ability to read with expression and intonation.
A student who struggles with prosody might read in “choppy” phrases or in a monotone voice. All three components are important for a child to become a fluent reader and improve their reading comprehension.
High-Frequency Sight Words
High-frequency words, or sight words, are words that show up frequently in language. They are used very frequently in books and when students are writing. It is very important that students learn these words with automaticity, meaning they know them as soon as they see them instead of taking the time to sound them out. Sight words show up so often in books that if a child does not know them quickly, it will affect their reading comprehension and fluency.
There are various lists used for high-frequency words, although the most popular are the Dolch list and the Fry list. These lists are separated into sets of 100 and taught to students in different grade levels. For example, students may learn the first 100 sight words in kindergarten and the second 100 in first grade.
Some examples of sight words include:
- the, of, and, is, in, you (usually taught in kindergarten)
- over, new, name, man, small (usually taught in first grade)
Reading: Literature and Informational Text
This section tests your knowledge on story elements, reading strategies used for comprehension, text features, and how to evaluate text complexity.
Here are some concepts that will be on the test.
Text organization, or text structure, is the way in which information is presented and organized in a book or reading passage. Information can be organized in various ways including:
- chronological order
- cause and effect
- problem and solution
Text that is organized in chronological order will present information in a sequence. It will have a beginning, middle, and end to the story. Narratives and fiction stories are generally organized in this way. Students can also look for transition words such as “first, next, and last” as a clue that a text was organized this way, although these transition words will not always be included.
Text that is organized by cause and effect will discuss something that happened and an event or consequence that happened because of this. An example of this would be a passage that talks about how animals are losing their habitats due to forests being cut down.
Text that is organized by problem and solution will have a problem that needs to be fixed and a solution, or way that the problem gets resolved. This can be easily confused with cause and effect. To use a similar example as the one above, text that is organized by problem and solution might discuss forests being cut down and then present possible solutions to this, such as designating land that cannot be disturbed.
Text organization can be identified by examining the way information is presented. Students can benefit from having graphic organizers available to think about how information was organized. You can encourage students in higher grade levels to take notes as they read and to mark important text features or story elements that can help them determine text structure.
Making inferences means combining information you have read with knowledge you already have to draw a conclusion about something. In order to make an inference, students need to be taught to think about what they know and what they read and then make a “smart guess” about what is happening.
An inference is different from a prediction because a prediction is thinking about what will happen next. Making an inference means drawing a conclusion about something even though it wasn’t explicitly stated. It is important that students are taught how to make inferences so that they can understand what they are reading, even when something is not directly stated or explained.
For example, let’s say a student reads this passage:
“John went to his friend’s house. They had cake and ice cream and his friend opened presents.”
The student would need to be able to make an inference that the boy went to a birthday party, even though this was never stated in the passage.
Text complexity is a way to determine how difficult or challenging a text will be for a student in a certain grade level. Text complexity is determined by three factors:
- qualitative measures of the text
- quantitative measures of the text
- factors related to the reader and the text
Qualitative measures are aspects that need to be considered about a text that cannot be measured in a concrete or quantitative way. This includes things such as inferences that a student would need to be able to make, necessary background knowledge, and the amount of support provided to the reader through pictures or definitions.
A teacher who is looking at the qualitative measures of a text might consider figurative language or a lack of pictures used in a text. For example, a book about the rainforest might include short and easy to decode words, but if the book does not have many pictures or uses a style of writing that the child is not used to, they will have a hard time comprehending what they have read.
Quantitative measures refers to aspects of the text that can be quantified, such as number of words, sentence length, or syllable length of words. Quantitative measures usually indicate a reading level, either by grade level or by another numerical designation.
Factors related to the reader and text refers to things such as student motivation and interests, as well as the complexity of questions that will be asked about the text. For example, a student who is interested in the rainforest will likely have an easier time reading a book about the rainforest than a student on the same reading level who has no interest in this topic.
This section tests your knowledge on common types of writing and their uses, developmental stages of writing that children go through, and the research process.
Take a look at these concepts.
Common Types of Writing
The common types of writing include expository, persuasive, narrative, and descriptive writing. Each type of writing is used for a different purpose and uses different formats and writing techniques to reach the intended audience.
Expository writing is used to inform or teach the reader about a specific topic. Expository writing uses facts and research, rather than descriptive detail. An example of expository writing would be a student’s research paper about penguins.
Persuasive writing is used to convince the reader to believe or do something. When students are writing a persuasive paper, they are taught to form an opinion on a topic and then convince the reader to agree with them by using facts and research or by appealing to the reader’s emotions. An example of persuasive writing might be an opinion article in a newspaper or an advertisement.
Narrative writing is writing that tells a story. It is one of the first types of writing that students learn to use. Narratives are written in sequential order and typically have a beginning, middle, and end. An example of narrative writing would be a student writing about their trip to the zoo and explaining what they did in sequential order.
Descriptive writing uses figures of speech and sensory language to give detail about an event, person, place, or thing. Students should be encouraged to use their five senses and descriptive words to help the reader create a mental image when they read. Poetry is a good example of descriptive writing.
Developmental Stages of Writing
The developmental stages of writing vary slightly in the name of each stage but typically identify similar milestones. These stages or milestones most often include:
- Using pictures and/or scribbles
- Using scribbles that begin to look more like the shape of letters
- Using random strings letters. For example, writing “I have a cat” as “VGTY”
- Using random letters with spacing to identify words, such as writing “I have a cat” as “V BG T PLG”
- Using initial consonants in writing, such as writing “I have a cat” as “i hb a cmg”
- Using initial and final consonant sounds in writing, such as “I hv a ct”
- Using vowel sounds in words, such as “I hav a cat”
- Using accurate spelling to form short sentences: “I have a cat”
Steps of the Research Process
The steps of the research process include:
- Identifying your topic: This is when you will decide on a topic you want to learn more about. For example, you might decide to research the habitat of penguins.
- Searching for resources: You will use various methods to search for resources that will help you learn more about your topic. This can include an internet search, locating books in the library, or finding videos about your topic.
- Gathering the materials needed to find information on your topic: This step goes hand in hand with the previous step. After you have searched for sources, you will gather these sources so that you can use them for research.
- Evaluating your sources: After you have gathered several sources, you will need to evaluate which sources are credible and most helpful for your research. For example, a website created by an unknown author will be less credible than a webpage from National Geographic.
- Compiling the information you have gathered: At this stage, you will gather your most helpful and reliable information to look through and find important information.
- Communicating the information gathered to your audience: This can take the form of a paper written about your topic, a web page, or a poster. It is important to understand your intended audience when you are doing this.
- Citing your sources: This shows where you obtained your information from. Depending on the purpose of the research project and the grade level of the students doing the research, citations may take on a slightly different format.
This section tests your knowledge on grammar, vocabulary, parts of speech, and the use of figurative language.
Let’s discuss some concepts that will more than likely appear on the test.
Parts of Speech
The different parts of speech include: nouns, pronouns, adjectives, verbs, adverbs, prepositions, and conjunctions. Each part of speech is described below.
Noun – A noun is a person, place, thing, or idea. A noun is a crucial part of a sentence because it tells who or what the sentence is about. A noun can be a common noun (a general word for something) or a proper noun (a specific name for something). Proper nouns begin with a capital letter. Examples of nouns include: boy, house, Jane, dog, pencil, Walmart.
Pronoun – A pronoun takes the place of a noun to avoid repetitive sentences. Examples of pronouns include: I, he, they, her, it, them.
Adjective – An adjective is a describing word. It is used to describe a noun or pronoun. Adjectives are helpful when a student is adding more detail and description to their writing. Examples of adjectives include: happy, large, beautiful, quiet, bumpy.
Verbs – Verbs are “action words” and are the main part of the predicate of a sentence. Verbs tell what the subject is doing or did. Examples of verbs include: jumped, run, draw, played.
Adverbs – Adverbs give more detail about a verb or adjective. Adverbs often tell how the subject did something. For example, in the sentence, “He ran quickly,” quickly is the adverb. Adverbs often end in -ly, but they do not have to. Examples of adverbs include: loudly, very, happily.
Prepositions – Prepositions are words that tell where or when something happens in relation to something else. In the sentence, “The boy is in the chair,” in is the preposition. Other prepositions include: beside, under, after.
Conjunctions – Conjunctions are words that are used to connect parts of a sentence or connect two sentences together. In the sentence, “She went to the store and bought milk,” and is the conjunction. Other conjunctions include: but, or, yet, so.
Figurative language is when words are used in a way that is different from their normal definition or use. Figurative language is used to make writing more interesting and descriptive. It includes similes, metaphors, onomatopoeia, hyperboles, and idioms.
- A simile is when one thing is compared to another by using the word “like” or “as.” An example of a simile is: “Her eyes were as bright as the stars.”
- A metaphor compares two things by stating that one thing is another. An example is: “Her eyes are stars.”
- An onomatopoeia is a word that is written to imitate a sound. Examples of onomatopoeia include: buzz, bark, plop.
- A hyperbole is an extreme exaggeration. An example is: “She was so hungry she could eat a horse.”
- An idiom is a phrase that has a meaning unrelated to the literal meaning of the words. Idioms can be difficult for English language learners or for students who have not been exposed to idioms in everyday conversation. Examples of idioms include: “I’m all ears,” and “It’s raining cats and dogs!”
3 Tiers of Vocabulary
The 3 tiers of vocabulary refers to different types of words and how often or in what manner they are used in oral language and in text.
Tier I words are words that are used in everyday language and conversation. These words generally do not need to be explicitly taught to students, because most children will already know the meaning of these words. Examples of Tier I words are: girl, book, play.
Tier II words are words seen frequently in text but are not used as often in everyday conversation. These words usually need to be taught to students, but after learning the meaning, they will be able to apply it to multiple texts or concepts. Examples of Tier II words are: analyze, evidence, infer.
Tier III words are academic words that are not used very often and typically only apply to specific topics. These words are often defined in a book’s glossary or the meaning is explained in the book. Examples of Tier III words are: exponent, ozone, constitution.
Speaking and Listening
This section tests your knowledge on effective methods of communication, including active listening and audience awareness.
Here’s a couple of concepts you may see on the test.
Active listening means truly focusing on what the speaker is saying and thinking about what is being said. It means you are giving your full attention to the speaker and making connections, thinking of questions, and evaluating what is being said. Active listening is an important part of learning. If students are actively listening, they should be able to restate or paraphrase what they hear. Asking students to restate what was said or explain something to another student is a good way to check for active listening.
Awareness of Audience
Having an awareness of your audience means that you consider who will be listening to you speak or who will be reading what you write. It means that you have adjusted the material you are presenting to fit the needs of your audience. For example, you would present material differently if you were speaking to a large group of college students instead of a small group of fifth graders, even if the topic of the presentation was the same.
It is important for teachers to be aware of their intended audience when planning lessons, but it is also important that students have an awareness of their audience when they are writing or presenting information. For example, a student writing a letter to a fellow classmate would write much differently than a student writing a letter to the principal of the school.
And that’s some basic info about the Reading and Language Arts content category.
The Mathematics content category has about 41 questions which make up about 29% of the test.
There are four Mathematics sections:
- Number and Operations
- Algebraic Thinking
- Geometry and Measurement
- Data, Statistics, and Probability
So, let’s start with Number and Operations.
Number and Operations
This section tests your knowledge on the base-ten number system, place value, basic mathematical processes, and the order of operations.
Let’s look at some concepts that may pop up on the test.
Expanded form is when a number is expressed by breaking the number down into the value of each digit. For example, the number 492 means that there are 4 hundreds, 9 tens, and 2 ones, so the expanded form of 492 would be:
400 + 90 + 2 = 492
Expanded form is an important part of understanding place value because students need to understand what each digit in a number is actually worth.
Other examples of expanded form are:
1,000 + 900 +30 + 4 = 1,934
70 + 3 = 73
800 + 50 + 2 = 852
Place value is the value of a digit based on where that digit is in the number. A digit is just a single whole number (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) in a number. For example, the number 29 has two digits (2 and 9). The number 138 has 3 digits (1, 3, and 8).
The place where a digit is located in a number determines its value. A place value chart, such as the one below, can help students understand how many ones, tens, hundreds, etc. are in a number.
For example, the number 4,712 has a 4 in the thousands place, a 7 in the hundreds place, a 1 in the tens place, and a 2 in the ones place. This means there are 4 thousands, 7 hundreds, 1 ten, and 4 ones in this number. The value of the 4 in the thousands place is 4,000 because the digit 4 is actually worth 4,000, not just 4 ones. Models and place value blocks can be helpful when teaching students about place value.
Here is an example of a place value chart for the number 2,356,703:
Order of Operations
The order of operations is the order in which computations must be completed in a math problem. The order of operations is as follows:
- Multiplication & Division
- Addition & Subtraction
This means that in a given math expression, anything that is contained within parenthesis must be completed first. After solving the expressions in the parenthesis, you would solve any part of the expression with an exponent. After the exponents, you would solve any multiplication or division portion of the problem, in the order they appear in the problem moving left to right. The last step is to solve any addition or subtraction parts of the problem, again moving left to right.
A common misconception about the order of operations is that multiplication comes before division and addition comes before subtraction. This is not the case. When you are at the multiplication and division step, you will solve whichever one comes first when you read the problem from left to right. The same thing applies to the addition and subtraction step. The order of operations can be remembered by the acronym PEMDAS.
Let’s work an example together:
30 – (7 – 3) x 5 + 4
- (7 – 3) would be solved first, because it is contained within parenthesis. The expression would now be: 30 – 4 x 5 + 4
- There are no exponents in this expression, so you would move on to multiplication and division and solve 4 x 5. The expression would now be: 30 – 20 + 4.
- The next step is addition and subtraction. Since the subtraction occurs first in this problem when read from left to right, you would do that first. The expression would now be 10 + 4.
- To complete the problem, you would solve 10 + 4 to get an answer of 14.
Properties of Operations
The properties of operations include the commutative property, associative property, and the distributive property. These properties refer to various strategies used to solve math equations.
The commutative property means that numbers can be added or multiplied in any order, and the answer will still be the same. For example, 4 + 7 + 3 will get the same result as 7 + 3 + 4. Similarly, 5 x 2 x 3 will get the same answer as 3 x 2 x 5. The commutative property does not apply to subtraction or division, because the answer will not be the same when the numbers are in a different order. For example, 5 – 2 will not get the same answer as 2 – 5.
The associative property means that numbers can be added or multiplied even when grouped in different ways, and the answer will still be the same. “Grouped” means put into parentheses for the purpose of the problem. For example, (6 x 2) x 4 will get the same answer as 6 x (2 x 4). Both expressions have a solution of 48. As with the commutative property, this does not apply to subtraction or division.
The distributive property means that you can multiply a number by the numbers or variables within the parentheses, and then find the sum. An example of the distributive property is shown below:
3(4 + 2)
Rather than doing 4 + 2 then multiplying this by 3, we can also do 3 x 4 then
3 x 2, and then add the two results:
3 x 4 + 3 x 2
12 + 6
The distributive property is most often used in problems with variables. An example of this is:
6(y + 4)
6y + 6 x 4
6y + 24
This section tests your knowledge on solving algebraic equations and your ability to analyze and interpret these solutions.
Let’s take a look at some concepts that you may see on the test.
Expression versus Equation
The main difference between an expression and equation is whether or not there is an equal sign. An equation contains an equal sign, while an expression does not. Both equations and expressions can have a solution, or answer, but only an equation will have an equal sign. For example:
16 + 4 = 20 is an equation.
16 + 4 is an expression.
Solving for x
Solving for x in an equation involves getting the x by itself on one side of the equation, leaving the answer (or value of x) on the other side. To do this, you will eliminate anything on the side with the x, one step at a time, in the reverse order of the order of operations. Since an equation must stay balanced, or equal, anything that you do to one side must also be done to the other side. Let’s look at an example, with explanations for each step:
3x + 4 = 13
To get x by itself on one side, we must get rid of the 4 that is being added, and the 3 that is being multiplied by x. Since the order of operations ends with addition and subtraction, and we are doing the reverse order, we will start by getting rid of the + 4 by doing the opposite of addition (subtraction). To do this, you will subtract 4 from each side of the equation:
3x + 4 – 4 = 13 – 4
This gets us to:
3x = 9
The 3 is still on the side of the equation with the x. Since the 3 is being multiplied by the x, we will do the opposite of multiplication and divide each side by 3:
3x ÷ 3 = 9 ÷ 3
3 divided by 3 is 1, but you do not need to put a 1 in front of the x since 1 times x would still be x. This now leaves us with the x on one side of the equation and 3 on the other side, meaning x is equal to 3:
x = 3
You can then check your work by putting this value for x back into the original equation to see if both sides are equal:
3(3) + 4 = 13
9 + 4 = 13
13 = 13
Since both sides of the equation are 13, we know our answer is correct.
Dependent versus Independent Variables
Independent and dependent variables are the variables used in data or an experiment. There are several ways to think about dependent and independent variables, but the main difference is that the dependent variable depends on the independent variable. The independent variable is the one that you can change, and the dependent variable is the one that will change based on the value of the independent variable.
Another way to think of this is to think of the independent variable as being the cause and the dependent variable as being the effect. In a set of data, the x-value will be the independent variable, and the y-value will be the dependent variable. For example, if a toy costs $5 and you are asked to find the total cost based on how many toys you buy, the equation used for this would be:
y = 5x
In this equation, y is the total cost of the toys, and x is the number of toys you buy. Since you control the number of toys you buy, this is an independent variable. The y-value (or total cost), however, depends on the number of toys you buy.
Geometry and Measurement
This section tests your knowledge on measurement and analysis of one-, two-, and three-dimensional figures and your knowledge on graphing and analyzing data using a coordinate plane.
Take a look at these concepts.
Surface area is the total area of all surfaces on a three-dimensional figure. Rather than memorizing formulas for surface areas of three-dimensional figures, it is easier to think about finding the area of each side, then adding these areas together for the total surface area.
Some basic formulas for areas of two-dimensional figures that might be helpful are:
Area of a square or rectangle = length x width
Area of a triangle = ½(base x height)
Area of a circle = r²
To find the surface of a rectangular prism, you find the area of each of the 6 sides and then add these values together. An example of this is shown below:
To find the surface area of this rectangular prism, you need to first find the area of each side. The area of the top and bottom are each 16cm2, since 4 x 4 = 16. The area of the four remaining sides are each 24cm², since 6 x 4 = 24. To find the total surface area, we need to add the area of each side together:
16 + 16 + 24 + 24 + 24 + 24 = 128
So, this rectangular prism has a total surface area of 128cm².
A coordinate plane is used as a way to show a visual representation of data points or an equation with variables. A coordinate plane is formed by an x-axis that runs horizontally (side to side) and a y-axis that runs vertically (up and down). The point where these two axes intersect is called the origin and has a coordinate of (0,0).
A coordinate is shown as two numbers in parenthesis, divided by a comma. The first number is the x-value and the second number is the y-value. The x-value shows how far over to go on the x-axis. The y-value shows how high up to go on the y-axis. The data point on the graph will be where these two lines meet. The coordinate plane below shows three examples of different data points.
A coordinate plane is divided into four quadrants. The four quadrants are labeled below:
Mass is how much matter is contained in an object. Although the actual definition of mass is slightly different than weight, mass and weight are very similar and mass is what we typically think of as weight. Mass is found by multiplying the volume of an object by its density. The following formula is used for mass:
Mass = Density x Volume
If an object has a volume of 50cm³ and a density of 2 grams/cm³, the mass would be 100 grams (50 x 2).
For general purposes, since mass typically has the same value as weight, you can also use a scale or balance to find an object’s mass.
A ray can be thought of as a straight line that has a starting point, but no ending point. A ray starts at a specific point but then continues in a certain direction to infinity. Rays are shown by a dot at the starting point and a line ending in an arrow, indicating that the line continues on with no ending point. Two rays can have the same starting point and then go in different directions. The coordinate plane below shows an example of two rays with the same starting point:
Data, Statistics, and Probability
This section tests your knowledge on basic statistics, data, and methods used to interpret this data.
Here are some concepts that are likely to pop up on the test.
Measures of Central Tendency
A measure of central tendency is a way to identify a typical value for a set of data. Ways to measure central tendency include mean, median, and mode:
Mean is another word for average. In order to find the mean for a set of numbers, you need to find the sum (or total) of all of the numbers, then divide that sum by the amount of numbers or values in the data set.
For example, to find the mean of 98, 95, and 83 you would add 98 + 95 + 83 to get 276. You would then divide 276 by 3 because there are 3 different numbers (98, 95, and 93). 276 divided by 3 equals 92, so the mean of this set of data is 92.
Median is the middle value when a set of numbers are put in order from least to greatest. If there is an even amount of numbers and two numbers are in the middle, you would find the average of those two numbers.
For example, to find the median of 34, 33, 38, 37, and 29, you would need to arrange the numbers in order from least to greatest:
29, 33, 34, 37, 38
Since 34 is in the middle, 34 is the median.
The following data set has two numbers that are in the middle:
12, 14, 15, 17, 20, 21
So, you would find the average of 15 and 17 to get a median of 16.
Mode is the number that appears most frequently in a set of numbers. For example, the mode of the following set of numbers is 18, because it appears 4 times in the set while other numbers appear one, two, or three times:
13, 10, 13, 18, 12, 12, 18, 18, 12, 18
If no number is repeated in a set, then that set of data has no mode.
A set of data can also have more than one mode if more than one number appears most frequently.
Probability means the likelihood of something happening. In order to determine the probability of something happening, you need to look at the total possible outcomes and the number of chances you have for one specific outcome occurring.
For example, if there are 3 pink pencils, 2 yellow pencils, and 5 blue pencils in a bag, there are 10 potential outcomes (10 different pencils). If you want to know the probability of choosing a pink pencil, you would set up a ratio, or fraction, showing the chance of choosing a pink pencil. Since there are 3 pink pencils and 10 pencils total, the probability of choosing a pink pencil would be 3/10 (or 3 out of 10).
And that’s some basic info about the Mathematics content category.
The Social Studies content category has about 25 questions which make up about 18% of the test.
There are six Social Studies sections:
- Geography, Anthropology, and Sociology
- World History
- United States History
- Government, Citizenship, and Democracy
- Social Studies as Inquiry and Social Studies Processes
So, let’s start with Geography, Anthropology, and Sociology.
Geography, Anthropology, and Sociology
This section tests your knowledge on important geographical features and how these features are represented on maps, as well as the impact of humans on the environment and vice versa.
Let’s look at some concepts you may see on the test.
Types of Maps
Various different types of maps can be used for different purposes. Some of the most common types of maps include political maps, topographical maps, physical maps, road maps, and climate maps. Each of these maps is explained in more detail below:
- Political Maps: Political maps are used to show boundaries, cities, states, counties, etc.
- Topographical Maps: Topographical maps show changes in elevation by using contour lines labeled with the elevation. When the lines are close together, it means there is a rapid or steep change in elevation. Topographical maps usually also show lakes or rivers. These maps are often used by hikers to navigate elevation changes.
- Physical Maps: Physical maps show the landscape of an area by showing the location of lakes, rivers, forests, and mountains. They sometimes indicate elevation change by using changes in color. If a physical map includes cities, it will usually only be larger or major cities in an area.
- Road Maps: Road maps are used for navigation. They show highways, streets, cities, and other important areas such as airports. They will sometimes show mile markers or exit numbers.
- Climate Maps: Climate maps indicate the temperature or climate in a certain area compared with other areas around it. Climate maps typically use color to show changes in climate.
Humans and the Environment
Humans change the natural environment in many ways. Some of these changes are small, such as people walking through a field and affecting some of the plant growth. Some of these changes are large and affect the earth in a major way, such as deforestation and emission of carbon dioxide. It is important that humans weigh the cost and the benefit to the changes they are going to make in the environment. For example, even though putting in a concrete sidewalk at a park will change the environment, the overall benefit will be that people follow a certain path and destroy less of the vegetation overall.
Natural resources are materials that occur naturally in the world and can be used for the benefit of humans, either for economic gain or not. They are resources provided by nature. Natural resources can be either renewable (resources we are able to make more of or reuse) or nonrenewable (resources that we are not able to make more of and can run out of). Some examples of natural resources include:
- Trees (renewable)
- Air (renewable)
- Water (renewable)
- Oil (nonrenewable)
- Coal (nonrenewable)
- Gas (nonrenewable)
It is important that we conserve and reuse our natural resources whenever possible by recycling or limiting our use of them. If we use too many natural resources we could use them up before we are able to make more of them, and we may negatively impact the land and animals that we are taking the resources from.
This section tests your knowledge on contributions from ancient civilizations, major wars, and events in recent history, and the process of globalization.
Let’s take a look at some concepts that might appear on the test.
Ancient Egyptians made many contributions to society. Some of the most notable contributions include:
- Paper, ink, and writing: The ancient Egyptians used papyrus as paper and moisture from plants as ink. They used hieroglyphics as a way to write and later developed an alphabet.
- Use of a clock and calendar: The ancient Egyptian calendar is very similar to our current calendar. It was made up of 360 days, divided into 12 months of 30 days each. Each day consisted of 24 hours.
- Historical documentation: The ancient Egyptians were one of the first known civilizations to document history.
- Agriculture and irrigation: Ancient Egyptians invented the plow and the hoe and created an irrigation system that took water for crops from the Nile River to canals.
World War II
World War II had many causes, but some of the main ones were: Hitler and the Nazi Party, instability and fascism in Europe, and Japanese expansion. World War II began in 1939 after Hitler invaded Poland. The United States entered the war in 1941 after the Japanese attack on Pearl Harbor. By the time World War II had ended in 1945, approximately 50 to 80 million people had died from war-related causes. Approximately six million of these people were Jewish and had been killed during the Holocaust.
Globalization refers to businesses and economies operating on a global scale. Advances in technology, the ability to outsource manufacturing, and the internet have allowed businesses to expand their reach into other countries and have employees from all across the globe. Globalization can have both positive and negative effects. For example, globalization has created more competition among industries, which creates better products and often lowers prices. However, it also creates job insecurity among people whose jobs are being outsourced to another country. It can also create tensions and legal issues between countries.
United States History
This section tests your knowledge on important events in United States history and the impact that these events had on our country.
Take a look at these concepts.
The Boston Tea Party
The Boston Tea Party was a protest led by a group of colonists in Boston called The Sons of Liberty. The colonists were protesting a tea tax that the British government was enforcing. Colonists went onto three British ships in the Boston harbor and dumped containers of tea into the harbor. Some well known Americans who participated in the Boston Tea Party were Samuel Adams, John Hancock, and Paul Revere. After finding out about the Boston Tea Party, Britain shut down the Boston harbor until all of the tea that had been dumped was paid for. They also implemented the “Intolerable Acts,” which increased tension between the colonists and Britain, eventually leading to the Revolutionary War.
Manifest Destiny was the idea or belief that American settlers were “destined” to expand their territories (and along with that, their democracy and economy) across North America. Manifest Destiny became a widely held belief among American colonists. This led to the expansion of American territories throughout what is now the western United States, but it also created problems with other countries and caused tension between American settlers and Native Americans.
The Underground Railroad
The Underground Railroad was a network of people, routes, and safe houses that helped slaves escape to freedom. The majority of the routes of the Underground Railroad ran from the southern United States to northern states or to Canada. The Underground Railroad happened mostly in the early to mid-1800s and led to approximately 100,000 slaves escaping to freedom during this time. Some of the most notable people who participated in the Underground Railroad were Harriet Tubman, Levi Coffin, and John Fairfield.
Government, Citizenship, and Democracy
This section tests your knowledge on the structure of the United States government, as well as important or well-known events in the history of our government.
Let’s look at some concepts that could appear on the test.
Federalism is a way of organizing a government. It is the type of government used in the United States. It means that an overarching government shares power with smaller governments within it. For example, the United States has sets of laws that all states must follow, but each state also gets power to create and implement many of their own laws.
Three Branches of Government
The United States government has three branches: executive, legislative, and judicial.
The executive branch consists of the president, vice president, federal agencies, and the president’s cabinet. The executive branch has the power and responsibility of enforcing and carrying out the laws that are created by the legislative branch.
The legislative branch consists of the members of Congress (the Senate and the House of Representatives). The legislative branch can propose new laws and can approve or reject presidential nominations for various roles, including nominations for the Supreme Court. The legislative branch also has the power to declare war.
The judicial branch consists of the Supreme Court and other federal courts. The judicial branch is responsible for interpreting and evaluating the law. The Supreme Court can apply laws to individual cases. They can also decide if a law is unconstitutional and if it is, they can overturn that law.
Articles of Confederation
The Articles of Confederation were created as the “first constitution” of the United States. They were approved by the Second Continental Congress in 1777 and became enforced in 1781 after being approved by all 13 states at the time.
One of the main goals of the Articles of Confederation was to limit the power of the central government and give more power to individual states. However, with so little power given to the central government, Congress was unable to effectively govern the states. Eventually, the American people decided that they needed a stronger central government, and in 1787 the Constitutional Convention met to change the Articles of Confederation. In 1789, the Articles of Confederation were replaced by the Constitution.
This section tests your knowledge on basic economic concepts, including supply and demand, how the economy impacts our lives, and how the economy and government interact with each other.
Let’s look at some concepts you need to know for the test.
Opportunity cost is something that must be given up in order to get something else. It can be thought of as the “trade-off” you must consider when making a choice between one thing or another. Opportunity cost can be monetary, a tangible item, or time. Some examples of opportunity cost are:
- A student chooses pizza instead of chicken nuggets in the lunch line. The chicken nuggets that were given up are the opportunity cost.
- You decide to stay home to study instead of going to a friend’s house. The opportunity cost is the time spent with your friend that you did not have.
- A business decides to use their advertising budget on social media instead of fliers. The opportunity cost is the fliers that were not made and the potential customers they might have reached.
Scarcity means having a limited supply of something. It occurs when there is not enough of an item or resource to fulfill a group’s wants and needs. When scarcity occurs, the cost of an item can increase due to a change in the supply. An example of scarcity is: There were not as many avocados produced this year, so there is a scarcity of avocados. As a result, the price of avocados will likely increase.
The Federal Reserve
The Federal Reserve is the central bank of the United States. The Federal Reserve helps regulate the economy by managing inflation, monitoring other banks, and by working with the Treasury Department to attempt to keep the economy stable.
Social Studies as Inquiry and Social Studies Processes
This section tests your knowledge on the process of researching and interpreting information related to social studies.
Here’s a concept you may see on the test.
Primary versus Secondary Sources
A primary source is a firsthand account of an event or firsthand description of a person. Primary sources include diaries, autobiographies, photographs, audio and video recordings, and historical speeches. A secondary source is something that interprets, comments on, or analyzes an event or person but does not contain firsthand information. Secondary sources include biographies, textbooks, and books written about an event by someone who was not there. Secondary sources often cite primary sources, but they can also cite other secondary sources, as well.
And that’s some basic info about the Social Studies content category.
The Science content category has about 25 questions which make up about 18% of the test.
There are five Science sections:
- Earth and Space Science
- Life Sciences
- Physical Sciences
- Impact of Science and Technology on Society
- Science as Inquiry and Science Processes
So, let’s start with Earth and Space Science.
Earth and Space Science
This section tests your knowledge on the structure of the Earth and its atmosphere, as well as processes that occur on Earth and in outer space.
Let’s look at some concepts that may appear on the test.
The earth’s magnetic field is created by electrical currents in the earth’s core. The magnetic field has two poles – a north and south pole. The magnetic field extends from these poles into space. It helps protect the earth from solar wind that could harm the ozone layer. The magnetic field also allows a compass to work, because the magnet in the compass will always point north.
The water cycle refers to the way in which water moves from land to bodies of water, to the atmosphere, and back to the land. The key components of the water cycle are described below:
- Precipitation: This is when water falls from the atmosphere onto land or bodies of water through rain, snow, sleet, or hail.
- Runoff: This occurs when water moves across land. This water can flow into rivers, lakes, or oceans, or it can seep into the soil or evaporate during the runoff process.
- Infiltration: This occurs when water on the surface of the land seeps into the soil or the ground.
- Evaporation: Evaporation happens when water changes from a liquid to a gas and enters the atmosphere. Evaporation can occur from oceans, rivers, lakes, or from water on the surface of land.
- Sublimation: Sublimation is when water changes directly from a solid to a gas, skipping the liquid state. The happens when snow or ice evaporates into the atmosphere without melting first.
- Condensation: This happens when water vapor in the atmosphere changes to liquid water droplets, forming clouds or fog.
Phases on the Moon
The different phases of the moon occur because of the different amounts of sunlight that reach the moon as it rotates around the Earth. The moon goes through one cycle of the moon phases about every month. The phases of the moon in order are:
- New moon
- Waxing crescent
- First quarter
- Waxing gibbous
- Full moon
- Waning gibbous
- Last quarter
- Waning crescent
The moon is considered “waxing” when the amount of the moon we can see is increasing. This occurs during the first half of the moon cycle. The moon is waning when the amount of the moon we can see is decreasing, or when the moon appears to be getting smaller each day. This occurs during the second half of the moon cycle. A picture of each moon phase is shown below:
This section tests your knowledge on the structure of living organisms and processes involved in these living organisms, including basic anatomy and physiology.
Let’s look at some concepts.
Photosynthesis is the process in which plants use sunlight, carbon dioxide, and water to create energy for the plant to grow. Plants take in water from the soil, carbon dioxide from the air, and light energy from the sun. The energy from the sun helps convert carbon dioxide and water into glucose (sugar) and oxygen. The plants use the glucose as energy for growth and the oxygen is released from the plant through the leaves.
Natural selection refers to the concept of living organisms with more favorable traits being more likely to survive, reproduce, and pass these favorable traits to their offspring. Natural selection plays an important role in evolution because it means that the organisms that are better equipped to adapt to their environment will be the ones that reproduce, therefore gradually changing the dominant traits in a species. For example, certain species of frogs have adapted over time to be better camouflaged in their environment, protecting them from predators. An example of natural selection that can be observed in a short time frame is the adaptation of certain bacteria to become resistant to antibiotics.
Types of Organisms
Different types of animal organisms include: mammals, birds, amphibians, reptiles, insects, and fish.
Mammals are warm-blooded animals with backbones (vertebrate), hair, and have the capability of producing milk for their offspring. Humans, dogs, and whales are all examples of mammals.
Birds are warm-blooded animals that lay eggs and have a backbone, feathers, and wings. Even though all birds have wings, not all birds are able to fly. Examples of birds include cardinals, eagles, and flamingos.
Amphibians are cold-blooded animals that begin their life in water and then eventually develop lungs to breathe outside of the water. Amphibians include frogs, toads, and salamanders.
Reptiles are cold-blooded vertebrates that have scales and usually lay eggs. Reptiles include snakes, lizards, and crocodiles.
Insects are invertebrates (they do not have a backbone) and have six legs, a body sectioned into three parts, and usually have wings. Examples of insects include ants, dragonflies, and termites.
Fish are cold-blooded vertebrate animals that live exclusively in water. They have gills that allow them to breathe underwater. Examples of fish include salmon, sharks, and stingrays.
Homeostasis refers to the body’s way of maintaining balance and equilibrium. Typically, homeostasis refers to keeping the body at a set temperature. If we become too hot or too cold, the body will go through processes as sweating or increasing blood flow to maintain a healthy temperature. Homeostasis can also refer to other processes in the body. For example, as glucose levels rise after eating, insulin and other mechanisms help process this glucose, keeping our glucose at a relatively consistent level. Homeostasis is an important way that we maintain a healthy and steady state.
This section tests your knowledge on properties of matter, chemical reactions, basic mechanics, and basic concepts of electricity, waves, and magnetism.
Let’s take a look at some concepts that may appear on the test.
Kinetic and Potential Energy
Kinetic energy is energy that an object has when it is in motion. Potential energy is stored energy or energy that an object has based on its location or position. When a sled is at the top of a hill but is not moving, the sled has potential energy. Once the sled is moving down the hill, the sled has kinetic energy. Energy can be converted back and forth from kinetic to potential energy by applying force to an object. For example, when you push the sled from the top of the hill, this converts the potential energy to kinetic energy. Pulling the sled back to the top of the hill converts the energy back into potential energy.
Heat transfer is the movement of heat from one space to another. Heat can be transferred in three ways: conduction, convection, and radiation.
Conduction is when heat is transferred through solids. When a pot is on the stove, the heat that is transferred from the burner to the pot is transferred through conduction.
Convection is when heat is transferred through a liquid or gas. Once the heat reaches the pot on the stove, that heat will be dispersed throughout the water via convection. A heater provides heat throughout a room by convection when the heat moves throughout the air in the room.
Radiation is when heat transfer happens through electromagnetic waves. One example of heat transfer from radiation is the heat that we feel from the sun.
Covalent versus Ionic Bonding
Covalent and ionic bonds are both ways in which atoms connect, or bond, to each other. The main difference is that covalent bonds are formed between two nonmetals, while ionic bonds form between a metal and a nonmetal.
In covalent bonds, the two atoms that are bonded together “share” electrons with each other. In ionic bonds, the nonmetal atom is stronger than the metal atom, and it “takes” an electron from the metal atom. A covalent bond is stronger than an ionic bond, meaning that it is easier to break the two atoms apart in an ionic bond. An example of a covalent bond is hydrochloric acid (HCl). An example of an ionic bond is Sodium Chloride (NaCl), better known as table salt.
The Doppler Effect
The Doppler Effect refers to the increase or decrease in intensity of sound or light waves as the source of the sound or light moves towards or away from someone. The most common example of the Doppler Effect is the increase in intensity and change in pitch of a siren as an ambulance or fire truck approaches and then passes by you. The Doppler Effect also played an important role in the Big Bang Theory, as it was able to show that galaxies were moving away from us, based on wavelengths.
Impact of Science and Technology on Society
This section tests your knowledge on the impact of scientific advances on the earth and on our daily lives.
Take a look at some concepts that may appear on the test.
Greenhouse gases are gases that trap heat in the atmosphere and contribute to the greenhouse effect. Too many of these greenhouse gases leads to heat getting trapped inside the atmosphere and contributes to global warming. Greenhouse gases can be man-made (such as chlorofluorocarbons, or CFCs), naturally occurring (such as water vapor), or both natural and man-made (such as carbon dioxide and methane).
Renewable versus Nonrenewable Energy Sources
Renewable resources are resources that we are able to make more of at a rate that is fast enough to replenish our use of them. Nonrenewable resources are resources that we are not able to make more of and could potentially run out of if we do not conserve them. Some examples of renewable resources include trees, air, and water. Examples of nonrenewable resources include oil, gas, and coal.
Genetically Modified Crops
Genetically modified crops or organisms (often referred to as GMOs) are plants that have been genetically altered using advancements in science and technology. Genetically modified crops use the desirable traits of a plant or other plants while eliminating many of the less desirable traits. Examples of genetically modified crops include most corn and soy, certain apples, and squash that is designed to resist insects. While genetically modified crops allow farmers to use fewer pesticides and produce more crops (therefore lowering the price of produce), many people are concerned that there have not been enough studies examining the long-term effects of GMOs on our health. Many studies have shown GMOs to be safe for human consumption, but the lack of long-term studies leaves people concerned and hesitant to consume GMOs.
Science as Inquiry and Science Processes
This section tests your knowledge on the scientific method, tools and procedures used in science experiments, and how to interpret results from experiments.
Let’s look at some concepts that may appear on the test.
The scientific method is used as a guide for conducting experiments and collecting data. The steps of the scientific method are described below:
- Ask a question/Develop a purpose for the experiment: At this stage, you are coming up with a question that you want to find an answer to. This question will drive your experiment. Your question should be something that can be measured. For example, a good question for an experiment might be: “How long will it take avocados to ripen in different situations?”
- Research: After coming up with a question, you will then research the topic to help you create a hypothesis. For example, you might research how avocados ripen or some ways to help them ripen faster.
- Create a hypothesis: The next step is to create a hypothesis, or educated guess, about what might happen in your experiment. Using the same example, your hypothesis might be, “I think the avocados will take 3 days to ripen on the shelf, 1 day to ripen in a paper bag, and 5 days to ripen in the fridge.”
- Design and conduct an experiment: At this stage, you will create an experiment that will help you answer your question and test your hypothesis. A good experiment for the avocados would be to purchase three avocados at the same ripeness and set one on the shelf, one in the fridge, and one in a paper bag, and then check the avocados each day for ripeness.
- Collect and analyze data: At this point, you will have data from your experiment that you can use to analyze and test your hypothesis. The main purpose of analyzing data is to see if your hypothesis was correct or if you need to do further experimenting.
- Conclusion: To conclude your experiment, you will report the data that you gathered and state if your hypothesis was correct or not. For example, your conclusion might state: “The avocado in the paper bag took 1 day to ripen, the avocado on the shelf took 2 days, and the avocado in the fridge took 5 days. My hypothesis about the avocados in the bag and fridge were correct, but my hypothesis about the avocado on the shelf was off by 1 day.”
Sir Isaac Newton
Sir Isaac Newton made major contributions towards the scientific revolution in the 17th century. Some of his most well-known contributions to science include:
- Newton’s Three Laws of Motion: Newton’s Three Laws of Motion state that:
- An object at rest remains at rest and an object in motion remains in motion unless acted upon by another force.
- Force is equal to mass x acceleration.
- For every action, there is an equal and opposite reaction.
- Newton’s Law of Universal Gravitation: Newton’s Law of Universal Gravitation was later replaced with Einstein’s Theory of General Relativity, but it was still a major contribution to our current understanding of gravity.
- Invention of the first reflecting telescope: The Newtonian telescope used mirrors instead of lenses, and was much more powerful than other telescopes being used at the time. This opened the door for more observations about outer space.
- Invention of calculus: Newton developed a mathematical theory, later recognized as calculus, that allowed mathematicians to study things (such as the slopes of curves) that algebra alone could not.
Standard Lab Safety Equipment
The basic lab safety equipment used in elementary classrooms are: goggles, gloves, aprons or protective clothing, fire extinguishers, and eye washing stations. Goggles, gloves, and aprons are used to protect from harmful objects or chemicals during an experiment. Fire extinguishers and eye washing stations are only used if needed during an emergency. Along with being familiar with the safety equipment, students should also be taught basic safety procedures, such as tying hair back during an experiment, reporting any spills to a teacher, and listening carefully to all instructions.
And that’s some basic info about the Science content category.
Reading and Language Arts
Which of the following sentences best demonstrates active listening?
- “I liked the movie because of all the famous actors and action sequences.”
- “How could you not like the movie?”
- “John thinks the movie overlooked the plot in favor of extended action sequences.”
- “I will write on my blog that the movie was entertaining.”
Correct answer: 3. Active listening is a process of being engaged and responding to another person in a way to build and improve communication. Active listeners spend more time listening than speaking. Paraphrasing someone else’s thoughts best demonstrates active listening because it demonstrates an understanding of another person’s communication.
How many phonemes are in the word “thought”?
Correct answer: 3. A phoneme is the smallest unit of speech that can be used to make one word different from another word. When two or more letters combine to create a sound, that sound is a single phoneme. The word “thought” has three phonemes because the word is composed of three distinct sounds: /th/, /ough/, /t/.
Which of the following phonemic awareness skills would be the last skill a student should be expected to master?
- Identifying suffixes and prefixes
- Removing syllables from the word
- Sounding out the word or blending phonemes
- Deleting phonemes
A teacher wants to develop reading fluency in his first-grade class. Which of the following would be the most effective activity to enhance the students’ reading fluency?
- Rereading stories that were used during a guided reading activity
- Engaging in a literary discussion group in the library
- Reading a book or essay on a level above the students’ independent reading levels
- Creating a graphic organizer after reading a student-chosen book
Correct answer: 1. Students acquire reading fluency and comprehension from books read during guided reading lessons with the teacher. Repeated readings from familiar books improve reading fluency.
While previewing a text, a fifth-grade student identifies the words “because”, “then”, and “therefore”. Which of the following comprehension skills is the student primarily using?
- Determining text structures
- Identifying perspective and bias
- Identifying text features
- Recognizing the genre of the text
Which of the following is the best definition of qualitative evaluation of text complexity?
- Qualitative evaluation analyzes the level of meaning, structure, language conventionality, clarity, and knowledge demands of a text
- Qualitative evaluation analyzes the readability measures and other scores of text complexity
- Qualitative evaluation analyzes the reader variables, such as motivation, knowledge, and experience of a reader
- Qualitative evaluation should not be used in analyzing text complexity
Correct answer: 1. Text complexity is simply how challenging text material is for the students at their specific grade level. Determining text complexity is important in proper assessment of students because the level will help the teacher understand how best to interpret students’ assessment scores. Qualitative evaluation of text complexity measures the qualitative dimensions of a text, such as the level of meaning, structure, language conventionality, and knowledge demands. Qualitative evaluation of text complexity seeks to understand how difficult a text is for the reader.
Read the following excerpt from a poem:
As an apple tree among the trees of the forest
so is my beloved among the young men.
With great delight, I saw in his shadow,
and his fruit was sweet to my taste.
The last line of the poem uses which type of language?
Correct answer: 2. “His fruit was sweet to my taste” is using figurative language to describe how the man is attractive and pleasant to the author. This is a use of figurative language.
A fourth-grade teacher presents students with the vocabulary word “scarce”. Which tier does this vocabulary word fit into?
- Tier 1
- Tier 2
- Tier 3
- Tier 4
Correct answer: 2. Tier 2 words are high frequency, multiple meaning words. These words are used in mature conversations and directly help and influence speaking and reading. “Scarce” is a Tier 2 vocabulary word for a fourth-grade student.
Which of the following is the best example of expository writing?
- A novel
- A research report
- A creative writing essay
Correct answer: 2. A research report is a good example of expository writing. Expository writing is writing in which the author’s purpose is to inform or explain the subject to the reader.
Read the following sentence:
Bill went to the store, but he did not buy anything.
In the sentence, the word “but” acts as which part of speech?
What is the value of the “3” in the number 17,436,825?
Correct answer: 1. In a base 10 system, each place location for a number has a value that is a power of 10. Specifically, the ones place is properly understood to be 10⁰ (because any nonzero number raised to the zero power equals 1). The tens place is 10¹, the hundreds place is 10², the thousands place is 10³, etc. In the opposite direction of the ones place, there is the tenths place from 10⁻¹ = 0.1 or 1/10, the hundredths place from 10⁻² = 0.01 or 1/100, the thousandths place from 10⁻³= 0.001 or 1/1,000, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position. Therefore, in the number 17,436,825, the 3 represents 3 x 10⁴, or 30,000.
The teacher provides a word problem for her students:
Quacky Donald’s Donuts sells glazed donuts in packages of six and donut holes in packages of 10. If Quacky Donald’s Donuts sold the same number of glazed donuts and donut holes yesterday, what is the minimum amount of donut holes that Quacky Donald’s Donuts sold?
Based on the world problem above, which of the following concepts is the teacher most likely to cover in the lesson?
- Least common factor
- Greatest common factor
- Least common multiple
- Greatest common multiple
Which expression best represents y in terms of x?
- y = x – 2
- y = 2x – 3
- y = 1 – 2x
- y = -(x + 4)
Mr. Andrews is in a city whose street grid can be represented by a coordinate plane. Mr. Andrews wants to walk from his current location at a local barbershop, represented on the coordinate plane as (1, 2), to his apartment. Mr. Andrews walks 5 blocks east, or to the right, and 1 block south, or down. Which of the following ordered pairs correctly depicts the location of Mr. Andrews’ apartment?
- (6, 0)
- (2, 7)
- (6, 1)
- (0, 7)
Correct answer: 3. The first number in the coordinates represents the X-axis, the second number represents the Y-axis. The X-axis runs horizontally and the Y-axis runs vertically. If Mr. Andrews walks 5 blocks east, or right, then it would be correct to add 5 to 1, which would be 6. If Mr. Andrews walks 1 block south, or down, then it would be correct to subtract 1 from 2, which would be 1. The correct answer is (6, 1).
Simplify: 15 – 3(8 – 6)²
Correct answer: 4. To get the correct final value of 3, the Order of Operations must be followed. In this problem, there are several operations occurring: subtraction, multiplication, and use of exponents. Because the order of operations, commonly abbreviated by the acronym PEMDAS, requires that what is inside parentheses be addressed first, the first step in this problem is to perform the subtraction of 8 – 6 = 2. From there, the problem becomes 15 – 3(2)². Once the work inside of the parentheses has been completed, exponents should be handled next. In this case, 2 is raised to the second power, resulting in 15 – 3(4). The subtraction and multiplication remain, but as “M” precedes “S” in PEMDAS, multiplication of the 3 with 4 must be completed before subtraction can occur, leaving 15 – 12 = 3. Note that a common error in this problem may include erroneously distributing the 3 from the front of the parentheses into the quantity “8 – 6” inside the parentheses. Because distributing 3 is a form of multiplication, and because exponents must be used before multiplication can occur, the 3 cannot be distributed to the quantity in the parentheses but must be multiplied only after the power is raised.
In the expression 3x² + 6x +3, what is the degree of 3x²?
Correct answer: 1. To find the degree of a monomial [(3x²) is a monomial – simply a single term in an equation], add the number of variables in the monomial. The monomial 3x² can be written: 3*x*x. There are two variables, so the degree of the term 3x² is two.
A third-grade teacher wants to assess students’ ability to calculate the area of non standard polygons. Which of the following figures would assess a student’s ability to find the area of non standard polygons?
- Figure 5
- Figure 10
- Figure 12 & 11 combined
- Figure 3
Jim wants to walk to Bill’s house. To get to Bill’s house, Jim walks 3 miles south and then walks 4 miles east. Jim wants to know how many miles he would have walked if he just walked in a straight line. How many miles would Jim have walked if he walked in a straight line to Bill’s house?
- 6 miles
- 7 miles
- 4 miles
- 5 miles
Correct answer: 4. This can be solved by using the Pythagorean Theorem: a² + b² = c². The Pythagorean Theorem allows students to find the length of any side of a right angle triangle when the length of the other two sides is known. Because Jim walked south, and then directly east, Jim makes a 90 degree turn. To find the distance if Jim walked straight, simply take the two lengths Jim walked and fill in the Pythagorean Theorem: (3²) + (4²) = 9 + 16 = 25 = (5²). C = 5.
Jessie draws a marble from the bag and then, without replacing the first marble, he draws a second one. What is the probability that he drew a red marble both times?
- 3/10 • 3/10
- 3/10 • 2/10
- 3/10 • 3/9
- 3/10 • 2/9
Correct answer: 4. This is an example of dependent events. P(red) = 3/10 for the first draw. In this situation the first marble is not returned to the bag, changing our sample to 9 marbles. If the first marble drawn was red, that leaves only 2 red marbles, so on the second draw, P(red) = 2/9; two red marbles out of 9 total. The probability of both events happening is 3/10 • 2/9.
What is the median and mean of the data set below?
10, 8, 5, 3, 7, 4, 5, 9, 2, 3, 7, 3, 8, 6, 4, 1, 2, 1, 10, 3
- Median: 7.0; Mean: 5.0
- Median: 3.5; Mean: 5.0
- Median: 4.5; Mean: 4.5
- Median: 4.5; Mean: 5.0
Correct answer: 4. Remember that before you can find the median, the data must be arranged in order from least to greatest or greatest to least. Then the median is simply the middle term. In this set, however, there are 20 terms so the middle two terms are 4 and 5. The median in this case is the average of the two middle scores: (4 + 5) ÷ 2 = 4.5. The mean is the sum of all of the numbers in the data set divided by 20, the number of items in the data set: 101 ÷ 20 = 5.02. The mean is about 5.0. The mean is written as 5.0 because the value has been rounded to the nearest tenth; writing the mean as 5 would indicate that it is an exact whole number, 5.
Which of the following types of maps shows a detailed and accurate graphic representation of cultural and natural features of the ground?
Correct answer: 3. A topographic map displays, in large detail, the cultural and natural features of the ground. In general, the purpose of topographic maps is to convey the relief, or elevation changes, in a particular area using contour lines.
Which of the following is the best example for showing the direct impact of human activities on the environment?
- Mountain lakes resulting from glacier runoff
- An oasis in the desert
- Destruction of an earthquake on urban environments
- Irrigation channels in agricultural communities
Which of the following is the greatest contribution of Greece to western society?
- Military strategy
- Democratic governance
Correct answer: 3. The foundations of democracy began in city-states of Greece, where male citizens were given an equal vote in legislative matters. The idea spread to the Roman Republic as citizens voted for their leaders. The political philosophy of Greek philosophers Aristotle and Plato would later influence philosophers, including John Locke, Benjamin Franklin, and Thomas Jefferson. While the other answer options are areas where Greece did influence western society, the idea of democratic governance is by the far the greatest as government creates and enforces laws.
One reason the American Revolution is significant in world history is because it:
- delayed the Industrial Revolution in Europe.
- ended British influence in the Western Hemisphere.
- set an example for future revolutions and constitutional governments.
- adopted reforms from the French Revolution.
Correct answer: 3. The American Revolution was one of the first successful revolutions where a colony gained independence from its parent country. Over the next hundred and fifty years, colonies in Asia, India, Africa, and Central and South America would begin their own revolutions to gain independence. As the countries gained independence, many established constitutional governments that emulated the Constitution crafted by our Founding Fathers.
Manifest Destiny inspired Americans to migrate westward and settle the land between the Mississippi River and the Pacific Ocean. Which of the following is a major long-term effect of this westward expansion by the United States?
- A peaceful relationship with American Indians
- Increased tensions between the United States and France
- Increased tensions between the United States and Great Britain
- The growth of agriculture and mineral operations in the United States
Correct answer: 4. This is correct. Much of the land settled by Americans in the 19th century was west of the Mississippi and the land was great for farming and had many natural resources, like gold, silver and oil, that Americans extracted.
The English desire for colonies in the Americas was directly influenced by:
- Mercantilism and the creation of joint-stock companies.
- Parliament’s increasing power during the 16th and 17th centuries.
- King James signing the Magna Carta.
- The Civil War between the Roundheads and the Cavaliers.
Correct answer: 1. Mercantilism was an economic philosophy that measured a nation’s wealth by the amount of gold it owned. In response to this philosophy, nations wanted to export more and import less (exports bring gold in, imports send gold out of the country). Nations began investing in colonies to diversify the nation’s resource production to maximize exports and minimize imports.
The division of power between the United States federal government and the states which compose the union of the United States demonstrates the principle of:
- checks and balances.
Correct answer: 3. Federalism is a political concept, or principle, of members joining together with a governing representative head. The states in the United States of America join together and are bound by a common federal government.
Which of the following is the best example of checks and balances in the U.S. government?
- The House of Representatives negotiates a treaty with England, the Senate approves the treaty, and the President signs it into law
- The judicial branch reviews legislation and can strike down laws that violate the U.S. Constitution
- The executive branch can nominate Supreme Court judges for impeachment and the legislative branch oversees the impeachment process
- The judicial branch can overturn Presidential vetoes with a 2/3 vote
Correct answer: 2. This is the best example of checks and balances. This concept is called judicial review; judicial review is the ability of the Supreme Court to strike down laws created by the Congress.
Mr. Scott breaks up a dispute among two second-grade students. In discussing the situation with the students, Mr. Scott realizes they were arguing over the use of class resources. This situation could best be used to teach which of the following economic principles?
- Opportunity cost
- Free trade
Correct answer: 1. Scarcity refers to the limitation of resources in a given scenario. Scarcity is a fundamental economic problem that humans have needs and desires, but they live in a world of limited resources. On a daily basis, humans must choose how best to spend their time to accomplish their priorities; humans cannot pursue all their desires and needs due to the limitation of time and resources. Scarcity leads to the idea of opportunity cost. A person must decide to pursue opportunity A or opportunity B and the cost of pursuing opportunity A is that opportunity B cannot be pursued (and vice-versa).
Which of the following best describes the importance of a primary source?
- They help researchers gain first-hand accounts and insights into a situation and allow researchers to draw conclusions based on the account
- They provide objective views of events after the date under study
- They help students read about the event in common, everyday language
- They provide students with concrete facts from which to draw logical conclusions
Which of the following would be the most effective strategy to reduce greenhouse gases?
- Reducing the use of fossil fuels
- Increasing the number of smokestacks to reduce emission per stack
- Adding lime to lakes that are highly acidic
- Developing greater irrigation for crops
Of the following, which best describes the lunar cycle as observed from the Earth?
- The orbit of the sun around the moon
- The orbit of the Earth around the sun
- The orbit of the moon around the Earth
- The reflection of Earth’s light onto the moon
Correct answer: 3. The lunar cycle is a result of the moon orbiting the Earth in relation to the sun. The illumination of the moon by the sun from the perspective of the Earth allows people on Earth to track the lunar cycle. As the moon orbits the Earth, different angles of the moon are visible from Earth because of how the moon is illuminated by the sun. This variance in illumination from the perspective of Earth results in people on Earth being able to monitor the orbit of the moon.
In the water cycle, energy from the sun heats the water, changing the liquid water into a gas. It loses energy and falls back to Earth. Which step in the water cycle is #4 in the diagram shown?
Correct answer: 1. In the water cycle, water on the Earth is heated by the sun and changes from a liquid to a gas, or water vapor (evaporates). The water vapor rises into the upper atmosphere where it cools and changes from a gas to a liquid, forming clouds (condensation). The air becomes saturated due to water in the air (humidity) and falls back to the Earth’s surface as a form of precipitation – rain, snow, sleet, or hail.
Many rodents living in the Sahara Desert have sand-colored hair. Which of the following best explains this phenomenon?
- Natural selection favors this color
- The sand caused a mutation to occur
- Sand-colored hair is easier for predators to see
- Because of the long days in the desert, the sun darkened their hair color
All living organisms are classified into one of the six kingdoms used in the modern-day classification system. The kingdoms are:
- atoms, cells, tissues, organs, organ systems, organisms.
- animals, plants, fungi, protist, eubacteria, archaebacteria.
- worms, fishes, birds, reptiles, amphibians, mammals.
- classes, phyla, orders, families, genus, species.
Jason was holding a ball and then threw it to Tommy, who caught the ball and held it in his glove before throwing it back. Which of the following represents a correct energy change as the boys played catch?
- During the catching of the ball, potential energy was constant
- As the ball was held and then thrown, kinetic energy was changed to potential energy
- Holding the ball and throwing the ball were both potential energy changed to kinetic energy
- Throwing the ball, then catching it showed kinetic energy changed to potential energy
Correct answer: 4. There are two forms of energy: kinetic energy – the energy of moving objects; and potential energy – stored energy. When a ball is held, its energy is stored. As the ball is thrown, its potential energy becomes kinetic energy.
A teacher is teaching a unit on weather to the class. As a demonstration the teacher heats a beaker on a hot plate and adds blue food coloring to the water. The students observe the movement of coloring in the water. Which of the following processes is best demonstrated by the movement of the food coloring?
Mr. Orlando is teaching a unit about density. He would like students to practice measuring the density of various objects. Which of the following lists of equipment should Mr. Orlando provide to his students?
- A microscope, beaker, and eye dropper
- A thermometer, a Bunsen burner, and a beaker
- A ruler, a rubber ball, and a tape measure
- A graduated cylinder and a balance
Correct answer: 4. Density is the relationship between the mass of a substance and its volume. A graduated cylinder will help the student measure volume and a balance will help the student measure mass.
Which of the following is the proper order for the taxonomic hierarchy?
- Kingdom, Phylum, Class, Family, Order, Genus, Species
- Kingdom, Phylum, Class, Order, Family, Genus, Species
- Phylum, Class, Kingdom, Family, Order, Species, Genus
- Class, Kingdom, Phylum, Order, Family, Genus, Species
Correct answer: 2. This is the correct order for the taxonomic rank. The taxonomic rank is a way to group species based upon relative, or common, characteristics. The more specific a group, the more characteristics animals within that classification share.
Which of the following is the basic structure of every living organism?
- Organ systems
Correct answer: 4. All living things have cells as their basic structure. Cells combine to make tissue, tissue combines to form organs, and organs group together to make organ systems.